The ∂-stabilization of a Heegaard splitting with distance at least 6 is unstabilized

Yanqing Zou; Qilong Guo; Ruifeng Qiu

doi:10.1007/s11401-014-0847-7

The ∂-stabilization of a Heegaard splitting with distance at least 6 is unstabilized

Yanqing Zou^*
, Qilong Guo
, Ruifeng Qiu

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let M be a compact orientable 3-manifold with ∂M connected. If V ∪_S W is a Heegaard splitting of M with distance at least 6, then the ∂-stabilization of V ∪_S W along ∂M is unstabilized. Hence M has at least two unstabilized Heegaard splittings with different genera. The basic tool is a result on disk complex given by Masur and Schleimer.

Original language	English
Pages (from-to)	557-562
Number of pages	6
Journal	Chinese Annals of Mathematics. Series B
Volume	35
Issue number	4
DOIs	https://doi.org/10.1007/s11401-014-0847-7
State	Published - Aug 2014

Keywords

Distance
Heegaard splitting
Stabilization

Access to Document

10.1007/s11401-014-0847-7

Cite this

@article{f18950ca6a7849989aecb192b1d97504,

title = "The ∂-stabilization of a Heegaard splitting with distance at least 6 is unstabilized",

abstract = "Let M be a compact orientable 3-manifold with ∂M connected. If V ∪S W is a Heegaard splitting of M with distance at least 6, then the ∂-stabilization of V ∪S W along ∂M is unstabilized. Hence M has at least two unstabilized Heegaard splittings with different genera. The basic tool is a result on disk complex given by Masur and Schleimer.",

keywords = "Distance, Heegaard splitting, Stabilization",

author = "Yanqing Zou and Qilong Guo and Ruifeng Qiu",

year = "2014",

month = aug,

doi = "10.1007/s11401-014-0847-7",

language = "英语",

volume = "35",

pages = "557--562",

journal = "Chinese Annals of Mathematics. Series B",

issn = "0252-9599",

publisher = "Springer Verlag",

number = "4",

}

TY - JOUR

T1 - The ∂-stabilization of a Heegaard splitting with distance at least 6 is unstabilized

AU - Zou, Yanqing

AU - Guo, Qilong

AU - Qiu, Ruifeng

PY - 2014/8

Y1 - 2014/8

N2 - Let M be a compact orientable 3-manifold with ∂M connected. If V ∪S W is a Heegaard splitting of M with distance at least 6, then the ∂-stabilization of V ∪S W along ∂M is unstabilized. Hence M has at least two unstabilized Heegaard splittings with different genera. The basic tool is a result on disk complex given by Masur and Schleimer.

AB - Let M be a compact orientable 3-manifold with ∂M connected. If V ∪S W is a Heegaard splitting of M with distance at least 6, then the ∂-stabilization of V ∪S W along ∂M is unstabilized. Hence M has at least two unstabilized Heegaard splittings with different genera. The basic tool is a result on disk complex given by Masur and Schleimer.

KW - Distance

KW - Heegaard splitting

KW - Stabilization

UR - https://www.scopus.com/pages/publications/84903841435

U2 - 10.1007/s11401-014-0847-7

DO - 10.1007/s11401-014-0847-7

M3 - 文章

AN - SCOPUS:84903841435

SN - 0252-9599

VL - 35

SP - 557

EP - 562

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 4

ER -

The ∂-stabilization of a Heegaard splitting with distance at least 6 is unstabilized

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this